Numerical investigations of the stepped double torsion fracture toughness specimen

This study aims at investigating the fracture behaviour of double torsion specimens using the finite element method. Typical double torsion tests encompass a series of constant-thickness specimens to evaluate the material plane strain fracture toughness. In contrast, the concept of using a novel variable thickness stepped specimen aims at deducing the fracture toughness using a single specimen. In this work, the feasibility of this approach is examined and the effect of the number of steps and fracture thickness in a specimen upon the resulting conditional stress intensity factor is evaluated. The finite element models employed experimentally determined values of the fracture load to evaluate the conditional stress intensity factor of the specimen. Finite element predictions were compared with earlier experimental results using both cast aluminium silicon alloy and gray cast iron specimens and good matching was observed between experimental results and numerical predictions.     

Numerical simulations of fracture-toughness improvement using short shaped head ductile fibers

Fibers can be shaped so as to anchor inside the matrix and resist pullout at a crack face, thus improving the fracture-toughness of the composites. This anchoring ability enables a greatly improved utilization of the plastic potential of ductile fibers, increasing fracture-toughness while maintaining stiffness. The purpose of this paper is to explore this property of shaped head fibers for composites with weak fiber–matrix bonding. Because of the difficulty in estimating the fracture-toughness contribution of shaped head fibers analytically or experimentally, we use a FEM based numerical scheme to investigate stress profiles induced during pullout of two chosen shaped head families. Annealed copper fiber with a large residual plastic potential and an elastic epoxy matrix have been used as representative materials. Using the computed strain energy distribution in the matrix as a measure of fracture-toughness contribution, we find that flat-head fibers out-perform ball-head fibers in minimizing failure potential. We have further discovered that within each shape family there exist optimal shapes. The optimal shape for the flat-head family is also computed for the example material system.     

FEA of crack-particle interactions during delamination in interlayer toughened polymer composites

A numerical analysis was conducted, using previously obtained experimental results, to establish basic toughening mechanisms and fracture behaviour of an interlayer-toughened composite material, containing particulate modified interlayers. Aims of the analysis were to examine the influence of the particles on the plastic zone size that develops in front of the crack tip and to investigate interactions between the particles and the crack tip during elastic-plastic crack propagation. Under both loading modes particles did not promote yielding but induced micro-cracking. This was concluded to be the most dominant toughening mechanism within high particle content interlayers.     

Numerical interpretation of cone crack initiation trends in a brittle coating on a compliant substrate

Finite element analysis is used to interpret trends in experimentally observed critical loads for contact damage in a brittle (porcelain) coating on a compliant (polymeric) substrate. Different forms of cracking in the brittle layer—both “cone” cracking initiating at the surface, and “radial” cracking at the layer/substrate interface—are considered, with varying coating thicknesses.

The resulting predicted critical loads agree qualitatively with the experimentally observed figures. It is postulated that a previously unexplained peak in critical loads for the onset of cone cracking is caused by a transition between differing modes of cone cracking.     

On the resistance to penetration of stiffened plates,Part II: Numerical analysis

A series of indentation tests have been carried out quasi-statically on various configurations of stiffened panels. These represent hull plates in ships subjected to grounding or collision actions. The results of the scaled down tests are reported in the first part of this two-part companion paper. This part (II) presents results from numerical analyses with focus on fracture prediction.     

Numerical aspects of cohesive-zone models

The importance of the cohesive-zone approach to analyse localisation and failure in engineering materials is emphasised and various ways to incorporate the cohesive-zone methodology in computational methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of this approach is demonstrated by some examples.     

Identification of material parameters for modelling delamination in the presence of fibre bridging

Delamination processes often exhibit an increase in delamination resistance, or R-curve, with crack extension. It is shown that cohesive laws can represent the R-curves due to large-scale fibre bridging and that the shape of the cohesive laws can be derived from conventional experimental results. Two approaches are investigated for determining the shape parameters of cohesive laws. The first approach consists of extracting the cohesive parameters from experimental R-curves through the use of a new semi-analytical equation. The second approach consists of a numerical optimization procedure that identifies material parameters by reducing the error between a finite element model and the experimental load–deflection results. The second approach is advantageous when fibre bridging introduces inaccuracies in the experimental energy release rate measurements. In addition, the second approach can be extended to allow more complex approximations of cohesive laws.     

The crack-modelling technique: optimization of parameters

The crack-modelling technique is a method for prediction of fatigue in components using finite element (FE) analysis. The technique, which is based on the estimation of equivalent K factors for stress-concentrators, has had some initial success in analysing components of complex shape, but this has raised a number of questions about the potential accuracy of the method and its sensitivity to the choice of operating parameters. The present paper reports on a systematic study using four different specimen types and one component geometry. Accurate estimates of equivalent K values are shown to be possible for both sharp notches and blunt notches, loaded in uniaxial tension or bending, using a very simple approach in which the stress distribution from the notch is compared to that from a standard cracked body. The method shows some sensitivity to the optimization routines used, and to some extent to the choice of the standard cracked body. It is relatively insensitive to mesh refinement and can be used with simple, elastic FE models.     

Fracture and physical properties of carbon anodes for the aluminum reduction cell

An experimental study with total 504 specimens has been carried out to investigate the fracture and physical properties of the carbon anode materials. The specimens were sampled from anodes produced with machined stub holes. From normal-and Weibull analysis the fracture toughness and the tensile strength showed a clear temperature dependency and orthotropic behavior. It has been found that both the fracture toughness and tensile strength increases with the temperature and are larger for the specimens directed in the horizontal direction than in the vertical direction. The variation in the tensile strength within an anode decreased with the temperature but the variation in the fracture strain increased. The tensile strain appears to be only dependent on the temperature and insensitive to the routine anode properties of the anode material. A multivariate linear regression analyses of the fracture toughness and tensile strength has been conducted and a typical correlation of R² = 0.5 (R is the Coefficient of Determination) to the measured routine anode properties was found. The thermal expansion coefficient is also larger in the vertical anode direction which makes the crack initiation more sensitive to temperatures. The orthotropic studies also showed that the air permeability has a tendency to be larger in the horizontal direction in the upper part of the anode which can induce unnecessary burning from the anode sides. The influence of the processing parameters in the paste plant and baking furnace has not been presented in this paper.     

The effect of stitch incline angle on mode I fracture toughness – Experimental and modelling

In this study, double cantilever beam (DCB) experiments were conducted to determine the effect of stitch incline angle on fracture toughness. The laminates were stitched with a square wave pattern having a pitch and spacing of 4 mm and three different angles being 0°, 22.5° and 45°. A semi-analytical model for DCB specimens was developed based on the Timoshenko beam theory and validated against the experiment results using a previously developed traction law. The results were also compared against a finite element analysis (FEA).     

Effect of fiber orientation on fracture toughness of laminated composite plates [0°/θ°]s

Fracture toughness of single edge notched fiber reinforced composite plates is investigated experimentally. Load–displacement curves for unidirectional carbon fiber/epoxy resin reinforced composite plates are obtained experimentally under tensile load. Fracture toughness is obtained by determining failure loads. For numerical study, ANSYS is used. Material properties of laminates are calculated with classical laminated plate theory and applied to the finite element model by using plane element. Stiffness matrix of laminates is determined and shell element is chosen for numerical solution. Critical stress intensity factors are calculated with Displacement Correlation Method under experimental failure load conditions.     

Fracture analysis of epoxy/SWCNT nanocomposite based on global–local finite element model

A global–local multiscale finite element method (FEM) is proposed to study the interaction of nanotubes and matrix at the nanoscale near a crack tip. A 3D FE model of a representative volume element (RVE) in crack tip is built. The effects of the length and chirality of single walled carbon nanotube (SWCNT) in a polymer matrix on the fracture behavior were studied in the presence of van der Waals (vdW) interaction as inter-phase region. Detailed results show that with increasing the weight percentage of SWCNT, fracture toughness improves. Three situations of nanotube directions with respect to crack are considered. Results show that bridging condition has minimum stress intensity factor. In addition, it can be seen that the crack resistance improves by increasing the length and chirality for all kinds of nanotubes. Finally, epoxy/SWCNT 10 wt.% has lower stress intensity factor compared to epoxy/halloysite 10 wt.% in similar loading state.     

Structural optimisation with fracture strength constraints

When considering the problem of shape optimisation with residual strength constraints it was recently found [1] that there were cases when the optimal shape for a body without an initial flaw was not the same as the optimal solution for a body with an initial flaw. It was also found that for the optimal case the stress intensity factors, for same length cracks emanating at right angles to any arbitrary point around the hole, were approximately constant along most of its circumference. As a result of this finding the present paper presents a new biological algorithm for the optimal design of structural components with fracture, i.e. residual strength, constraints. This approach is illustrated by considering the problem of an optimum cut-out geometry for a rectangular plate subjected to a bi-axial stress field and the problem of the shape optimisation of a fillet with residual strength constraints.     

Evaluating the linear normalization technique for deriving J-resistance curves

In this paper, results from the linear normalization (LN) technique of Reese and Schwalbe for deriving J‐crack resistance (J–R) curves have been compared, related to J–Δa (J‐integral–ductile crack growth) data points, to those obtained from traditional elastic compliance technique. Research results regarding a nuclear grade steel exhibiting a wide range of elastic–plastic fracture resistance agree quite well for both techniques until a certain level of toughness of the material. Below this critical level, LN produces inconsistent results for the sub‐sized compact tension specimens (0.4T C[T]). The evidence suggests that the loss of applicability of the LN technique can be determined on the basis of the η plastic factor (η_pl) for the best linear correlation achieved for ΔP_N–Δa (normalised load gradient–ductile crack growth) data.     

A hybrid formulation for 3D fracture analysis

Structures with multiple load paths experiencing either isolated cracking, widespread fatigue damage or repairs to multi-site damage can experience changes in the load path resulting from changes in stiffness due to either the cracking or the associated structural repair. To account for this effect, the present paper develops a new 3D hybrid formulation capable of representing this change in stiffness, thereby enabling an accurate analysis of multiple load path structures containing three-dimensional flaws. This formulation has been prompted by the advent of cluster based computing which means that it is now desirable to develop new computational techniques for assessing structural integrity. This procedure has been validated by comparison with results available in literature and with results obtained using the alternating finite element technique. For the surface crack problems considered it was found that, if symmetry considerations were used, then accurate results could be obtained with only 65 elements, including the “hybrid element”.     

Numerical analysis on the interaction of guided Lamb waves with a local elastic stiffness reduction in quasi-isotropic composite plate structures

This paper investigates how Lamb waves respond to the presence of material degradation in a plate-like structure using a series of finite element analyses. To facilitate this study, the propagation of these guided waves was interpreted with the dispersion characteristics and displacement profiles were analysed in the frequency and wave number domain. The results show that the material degradation simulated by a local stiffness reduction which leads to changes in the dispersive characteristic of the propagating waves has made the Lamb waves technique become an effective tool to assess the material degradation.     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

On the fitting and extrapolation of J-resistance data derived through the linear normalization technique

In this paper, an assessment is made regarding the effects of J–R curve fitting and extrapolation methods in two J‐integral criteria – namely crack initiation, J_i, and tearing instability, J₅₀– which were obtained through the linear normalization technique. Power‐law, logarithmic and linear fits were concurrently applied to J–Δa data derived from sub‐sized compact tensile specimens machined from a nuclear grade steel and tested at 300 °C. Research results show that the logarithmic J–R fit is the most conservative approach within a broad range of elastic–plastic fracture resistance, compared to the conventional power‐law fit. On the other hand, the linear fitting method provided the most non‐conservative J‐predictions. The values of J_i and J₅₀ have been successfully correlated with the net energy absorbed during Charpy impact testing of the materials.     

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.